Geodesic
Estimation of the growth of the degree of nonconvexity of reachable sets in terms of $\alpha$-sets
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 100-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the properties of $\alpha$-sets, which are a generalization of convex sets. The relationship between $\alpha$-sets and weakly convex sets is established in the sense of Vial and Efimov–Stechkin. An estimate of the growth over time of the nonconvexity measure $\alpha$ of reachable sets is obtained for one class of control systems in a two-dimensional state space.
Keywords: generalized convex set, weakly convex set, reachable set, control system.
Mots-clés : $\alpha$-set 
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V. N. Ushakov; A. A. Ershov. Estimation of the growth of the degree of nonconvexity of reachable sets in terms of $\alpha$-sets. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 100-106. http://geodesic.mathdoc.fr/item/DANMA_2020_495_a20/

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